Simple Harmonic Motion (SHM) describes a type of periodic, oscillatory motion where an object moves back and forth around an equilibrium position in a smooth, repetitive pattern. Common examples include a mass attached to a spring and a pendulum swinging.
Key Characteristics:
- The motion is periodic, meaning it repeats at regular time intervals called the period.
- The restoring force that brings the object back toward equilibrium is directly proportional to the displacement but acts in the opposite direction (Hooke’s Law).
- The displacement, velocity, and acceleration vary sinusoidally with time.
Examples:
- A mass on a spring stretches or compresses, then oscillates due to the spring’s restoring force.
- A pendulum swings back and forth under the influence of gravity, approximating SHM for small angles.
Important Features:
- The amplitude is the maximum displacement from equilibrium.
- The frequency is how many oscillations occur per unit time.
- The angular frequency relates to the speed of oscillation and depends on system properties like mass and spring stiffness.
Applications:
- SHM models many natural phenomena, including vibrations of molecules, sound waves, and electrical circuits.
- It provides the foundation for understanding more complex wave and oscillation systems.